In his brilliant, aphoristic demolition of the modern, Pure: Modernity, Philosophy and the One, philosopher Mark Anderson explains in a few short paragraphs why nature cannot explain nature:
A particle of matter is because of an act of existence for which it itself is not responsible. It is what it is because of its microstructure, the specific and stable organization of its constitutive elements – in a word, its form, which it itself does not produce. The same is true, mutatis mutandis, of forces and laws of nature, which neither bring themselves into being nor cause their specific and essential character.
The materialist would like to explain the world in full by means of the attributes and arrangements of material particles in conjunction with natural forces and the laws that determine their appearance and application. But any such explanation necessarily presupposes the existence and ordered constitution of the particles, the forces, and the laws themselves. Matter and its properties, natural forces and the laws that govern them, are neither self-generating nor self-explanatory; they depend utterly upon the ontologically prior acts of existence and form. Without these metaphysical principles there can be no physical reality.
Moral: physics, being derivative, will never provide the fundamental explanation of reality. [p. 37 ff.]
JR Lucas argues that this incapacity of natural history to explain itself is entailed by Gödel’s Incompleteness Theorem. Gödel showed that every consistent formal system or logical calculus that is adequate at least to simple arithmetic (that, i.e., contains the natural numbers and the operations of addition and subtraction), is capable of generating true statements that cannot be demonstrated in the terms of the calculus. Thus no formal system is capable of demonstrating all the truths that it can express; formal systems are all therefore incomplete.
[Gödel has proved] that a human being cannot produce a formal proof of the consistency of a logistic calculus inside the calculus itself: but there is no objection to going outside the logistic calculus and no objection to producing informal arguments for the consistency either of a logistic calculus or of something less formal and less systematized. Such informal arguments will not be able to be completely formalised: but then the whole tenor of Gödel’s results is that we ought not to ask, and cannot obtain, complete formalisation. [The Freedom of the Will, p. 162]
Lucas then cashes out his argument:
If we are consistent and can say that we are, it follows without more ado from Gödel’s second theorem that we cannot be completely described as physical systems instantiating some logistic calculus. [ibid]
In proposing this argument, Lucas was concerned primarily to demonstrate the freedom of the human will. If no formal system can completely describe us, then no logic – such as the logic and order concretely embodied in, and expressed by, the past – can completely determine us. But it is easy to see, as Lucas certainly did, how this argument applies likewise equally for any system of concrete actualities, whether physically implemented or purely immaterial. No consistent logical calculus can be completed. But then, any system of concrete actualities that instantiates a consistent logical calculus – which is to say, any system of things, any world, or any portion of any world, that is either causally coherent and orderly on the one hand, or intelligible on the other – can complete its own description.
To say that no world’s logic can fully account for itself is just to say that no world can cadge together a complete causal account of itself. But note then that to say that a world cannot wholly account for itself causally is ipso facto just to say that it cannot wholly cause itself. Worlds as such, then, stand in need of creators.
Thus not only is it impossible for science to explain or justify science, but it is impossible to complete the scientific formalisation – that is to say, the rigorous scientific understanding – of the world, or for that matter any portion of any world. So, science begins in mystery, issues from and proceeds in mystery, and must always point to mystery.